1A. Renyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest 2Department of Mathematical and Statistical Sciences, University of Colorado Denver, Colorado, Denver 3Delft Institute of Applied Mathematics, Delft University of Technology, PO-box 5, 2600AA, Delft
The electronic journal of combinatorics, Tome 24 (2017) no. 2
In 2008 Amanatidis, Green and Mihail introduced the Joint Degree Matrix (JDM) model to capture the fundamental difference in assortativity of networks in nature studied by the physical and life sciences and social networks studied in the social sciences. In 2014 Czabarka proposed a direct generalization of the JDM model, the Partition Adjacency Matrix (PAM) model. In the PAM model the vertices have specified degrees, and the vertex set itself is partitioned into classes. For each pair of vertex classes the number of edges between the classes in a graph realization is prescribed. In this paper we apply the new skeleton graph model to describe the same information as the PAM model. Our model is more convenient for handling problems with low number of partition classes or with special topological restrictions among the classes. We investigate two particular cases in detail: (i) when there are only two vertex classes and (ii) when the skeleton graph contains at most one cycle.
Péter L. Erdős
1
;
Stephen G. Hartke
2
;
Leo van Iersel
3
;
István Miklós
1
1
A. Renyi Institute of Mathematics,
Hungarian Academy of Sciences,
Budapest
2
Department of Mathematical and Statistical Sciences, University of Colorado Denver, Colorado, Denver
3
Delft Institute of Applied Mathematics, Delft University of Technology, PO-box 5, 2600AA, Delft
@article{10_37236_5459,
author = {P\'eter L. Erd\H{o}s and Stephen G. Hartke and Leo van Iersel and Istv\'an Mikl\'os},
title = {Graph realizations constrained by skeleton graphs},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {2},
doi = {10.37236/5459},
zbl = {1366.05027},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5459/}
}
TY - JOUR
AU - Péter L. Erdős
AU - Stephen G. Hartke
AU - Leo van Iersel
AU - István Miklós
TI - Graph realizations constrained by skeleton graphs
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/5459/
DO - 10.37236/5459
ID - 10_37236_5459
ER -
%0 Journal Article
%A Péter L. Erdős
%A Stephen G. Hartke
%A Leo van Iersel
%A István Miklós
%T Graph realizations constrained by skeleton graphs
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/5459/
%R 10.37236/5459
%F 10_37236_5459
Péter L. Erdős; Stephen G. Hartke; Leo van Iersel; István Miklós. Graph realizations constrained by skeleton graphs. The electronic journal of combinatorics, Tome 24 (2017) no. 2. doi: 10.37236/5459
